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The curve is an equiangular or logarithmic spiral. Large
guns are built of coils shrunk one over the other, so as to put
the inner tube in a state of compression. The pressure of the
explosion then tends to equalise the stress, by slightly adding to
the outer tension, but more than removes the inner compression.
When cold, a coil is slightly smaller than the core it is to envelop,
according to the following rule :

TX.   .     .        ,..,-.       meandia.2xr
Diminution of coil dia. =-

inside dia.


c for the outer coils =
c for next inner coils =
c for next inner coils =

= -00133
-• "00108

: '00083

Let an outer coil be 17" outside and 12" inside, then

x *°OI33
- ±*

T-V   •      •
Diminution =



The same effect is produced in cast-iron cylinders by casting with
a cold-water core, and thus much less thickness is required. (See
Figs. 289, 298, 299, 300.) (See Appendices I. and //., //. 757
and 841.)

< Casting Rule ' for Steam Cylinders, &c.— With the
usual steam and gas pressures, the previous formulae give so small
a thickness that the metal would not fill the sand mould during
casting, so an empirical rule must be adopted to enable the
cylinder or gas pipe to be cast, thus :

This will represent the thickness of steam chest and other parts,
but the cylinder body should be about J in. thicker, to allow
for reboring, and the flanges should also be stiffer.

Tensile Stress induced by Centrifugal Force.—
When a weight a/, attached to a string, is swung in a circular
path, it exerts a pull upon the string represented by the formula

>s.    (where v=actual velocity of weight)

In a grindstone or flywheel this centrifugal pull exerts a tension
between the particles of the material, which we shall examine in